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We introduce a class of absolutely continuous bivariate exponential distributions, generated from quadratic forms of standard multivariate normal variates. This class is quite flexible and tractable, since it is regulated by two parameters only, derived from the matrices of the quadratic forms: the correlation and the correlation of the squares of marginal components. A simple representation of the whole class is given in terms of 4-dimensional matrices. Integral forms allow evaluating the distribution function and the density function in most of the cases. The class is introduced as a subclass of bivariate distributions with chi-square marginals; bounds for the dimension of the generating normal variable are underlined in the general case. Finally, we sketch the extension to the multivariate case.
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